S = [
0.004
0.002
0.001
0.0005
];
R = [
104.601
85.5107
1.92629
2.54268
];
T = [
2.087
4.192
6.608
13.405
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
29.3421
101.928
1.78555
2.05385
];
T = [
2.468
5.927
12.543
25.042
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
66.866
1.22155
1.75243
0.507994
];
T = [
4.958
8.03
15.853
29.896
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
288.897
1.68279
1.73459
1.50241
];
T = [
7.231
9.996
18.619
28.824
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(2);
legend('s = 1','s = 2','s = 3','s = 4');
saveas(gcf,'pictures/test198/AdamsBashforth198_T.png');
figure(2);
clf;
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.72206
1.2659
1.74278
1.70071
];
T = [
2.303
3.535
9.988
13.414
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
16.0234
2.0561
2.12927
0.278681
];
T = [
2.34
6.215
12.767
22.463
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
1.6865
1.59422
10.7604
1.07677
];
T = [
4.564
8.195
15.274
28.693
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
1.62331
2.02937
1.16482
0.280049
];
T = [
5.418
10.577
18.341
36.48
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(2);
legend('s = 1','s = 2','s = 3','s = 4');
saveas(gcf,'pictures/test198/AdamsMoulton198_T.png');
figure(2);
clf;
S = [
0.004
0.002
0.001
0.0005
];
R = [
122.354
198.695
780.082
11.1805
];
T = [
2.136
6.865
11.888
13.208
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.59553
1.11108
2.32182
1.75003
];
T = [
3.619
6.16
11.183
17.008
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
43.8056
2.55334
2.06695
9.93672
];
T = [
3.967
7.521
15.338
31.284
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
1.4467
1.73556
0.654675
0.978601
];
T = [
6.459
10.971
17.932
37.414
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(2);
legend('s = 1','s = 2','s = 3','s = 4');
saveas(gcf,'pictures/test198/BDFs198_T.png');
figure(2);
clf;
figure(1);
X = [
0.994
0.993961
0.993845
0.993658
0.993407
0.993102
0.992752
0.992365
0.991949
0.991509
0.991052
0.990582
0.990101
0.989613
0.98912
0.988623
0.988124
0.987623
0.987122
0.986622
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0.985624
0.985127
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0.981707
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0.0404783
0.040444
0.0404091
0.0403736
0.0403377
0.0403012
0.0402642
0.0402267
0.0401887
0.0401501
0.040111
0.0400714
0.0400312
0.0399905
0.0399492
0.0399074
0.039865
0.0398221
0.0397786
0.0397346
0.03969
0.0396449
0.0395991
0.0395529
0.039506
0.0394586
0.0394106
0.039362
0.0393128
0.0392631
0.0392127
0.0391618
0.0391103
0.0390582
0.0390055
0.0389521
0.0388982
0.0388436
0.0387885
0.0387327
0.0386763
0.0386193
0.0385616
0.0385033
0.0384444
0.0383848
0.0383246
0.0382638
0.0382023
0.0381401
0.0380773
0.0380138
0.0379496
0.0378848
0.0378193
0.0377531
0.0376862
0.0376186
0.0375503
0.0374814
0.0374117
0.0373413
0.0372702
0.0371984
0.0371258
0.0370525
0.0369785
0.0369037
0.0368282
0.036752
0.0366749
0.0365971
0.0365186
0.0364392
0.0363591
0.0362782
0.0361965
0.0361139
0.0360306
0.0359465
0.0358615
0.0357757
0.035689
0.0356015
0.0355132
0.035424
0.0353339
0.0352429
0.0351511
0.0350584
0.0349647
0.0348702
0.0347747
0.0346783
0.0345809
0.0344826
0.0343834
0.0342832
0.034182
0.0340798
0.0339766
0.0338724
0.0337672
0.0336609
0.0335536
0.0334452
0.0333358
0.0332253
0.0331137
0.033001
0.0328871
0.0327721
0.032656
0.0325387
0.0324202
0.0323006
0.0321797
0.0320576
0.0319342
0.0318096
0.0316837
0.0315565
0.031428
0.0312982
0.031167
0.0310344
0.0309005
0.0307651
0.0306283
0.03049
0.0303502
0.0302089
0.0300661
0.0299217
0.0297758
0.0296282
0.029479
0.0293281
0.0291755
0.0290212
0.0288651
0.0287072
0.0285474
0.0283858
0.0282223
0.0280568
0.0278894
0.0277199
0.0275483
0.0273747
0.0271988
0.0270208
0.0268404
0.0266578
0.0264728
0.0262853
0.0260954
0.0259029
0.0257078
0.02551
0.0253095
0.0251061
0.0248998
0.0246905
0.0244781
0.0242625
0.0240437
0.0238215
0.0235958
0.0233666
0.0231336
0.0228968
0.0226561
0.0224112
0.0221621
0.0219086
0.0216505
0.0213877
0.0211199
0.020847
0.0205687
0.0202848
0.0199951
0.0196994
0.0193972
0.0190883
0.0187724
0.0184492
0.0181182
0.017779
0.0174312
0.0170743
0.0167077
0.0163309
0.0159431
0.0155438
0.0151321
0.0147072
0.0142681
0.0138138
0.0133431
0.0128548
0.0123474
0.0118193
0.0112689
0.0106942
0.010093
0.00946321
0.00880228
0.00810772
0.00737699
0.00660776
0.00579816
0.00494717
0.00405521
0.00312471
0.00216076
0.0011714
0.000167376
];
plot(X,Y,'k');
xlim([-1.5 1.2]);
ylim([-1.2 1.2]);
ax = gca;
box off;
ax.Position = [0.05 0.05 0.9 0.9];
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
ax.XTickLabel = {};
ax.YTickLabel = {};
h = title('ClassicalRK4');
h.Interpreter = 'latex';
saveas(gcf,'pictures/test198/ClassicalRK198_4.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
1.94733
1.9879
0.856771
0.0255064
];
T = [
10.859
22.175
36.854
61.832
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test198/ClassicalRK198_T.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.03585
4.72042
0.171554
0.0545707
];
T = [
26.711
45.494
84.833
173.964
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test198/ESDIRK198_T.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.07105
0.166239
0.151208
0.0736849
];
T = [
21.088
42.675
84.225
169.723
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test198/Fehlberg198_T.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.05421
0.391957
0.117327
0.0710093
];
T = [
28.83
56.733
115.942
230.161
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
saveas(gcf,'pictures/test198/DormandPrince198_T.png');
S = [
0.004
0.002
0.001
0.0005
];
R = [
63.3875
1.76509
1.96113
2.03086
];
T = [
1.151
1.721
3.449
6.836
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
2.04324
1.72628
0.0776468
0.0591942
];
T = [
2.93
5.667
10.946
22.701
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
S = [
0.004
0.002
0.001
0.0005
];
R = [
0.533756
0.315402
0.067068
0.0680468
];
T = [
5.959
11.789
24.122
47.6
];
figure(2);
subplot(1,2,1);
semilogy(S,R);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('Log of Max-norm Error');
subplot(1,2,2);
plot(S,T);
set(gca,'XDir','reverse');
xlabel('Time Step');
ylabel('CPU Time');
figure(2);
subplot(1,2,1);
hold on;
subplot(1,2,2);
hold on;
figure(2);
legend('s = 1','s = 2','s = 3');
saveas(gcf,'pictures/test198/GaussLegendre198_T.png');
